A computer algebra system is recommended. A manufacturer of corrugated metal roofing wants to produce panels that are 48 in. wide and 2 in. high by processing at sheets of metal, as shown in the figure. -!l The profile of the roofing takes the shape of a sine wave and the sine curve has the equation y = sin( 2in 'l (D 'X ). Find the width w (in inches) of a at metal sheet that is 12 needed to make a 48-inch panel. (Numerically evaluate the integral correct to two decimal places.) 49.03 x in. Need Help? The figure shows a telephone wire hanging between two poles at x = 35 and x = 35. The wire hangs in the shape of a catenary described by the equation given. y = c + a cosh() a \\\\ n '\\\\ 35 0 35 X (D If the length of the wire between the two poles is 71 ft and the lowest point of the wire must be 16 ft above the ground, how high up (in ft) on each pole should the wire be attached? (Round your answer to two decimal places.) 21.07 x ft \\wail Ii: :i-9' Rndll x The arc length function for a curve y = f(x), where f is an increasing function, is s(x) = 5t + 10 dt. (a) If f has y-intercept 5, find an equation for f. f ( x ) = is ( 5x + 9 ) + (b) What point on the graph of f is 4 units along the curve from the y-intercept? State your answer rounded to 3 decimal places. ( x, y ) = 1.120 X Need Help? Read It4 units along the curve from -intercept,.i.e.x=0, X s(X) = 4 = / V5t + 10dt Upon Integration we get, 2 V5(x + 2)# - 2V10 # 4 = 3 # 6 = V5(x + 2)# - 2V10 76 + 2410 # X = -2 = 1.12026 5Given arc length function, s(x) = / V5t + 10dt Differentiate using fundamental theorem of calculus, ds dx = V5x + 10 But arc derivative of arc length is , ds x = V1+(y)> Then equating both we get, # V1+ (y )2 = v5x + 10 2 = 5x + 9 dx dy = +v5x + 9 dx Consider only positive value since y=f(x) is increasing, dy = V5x + 9 dx y = / (5x +9)0.5dx (5x + 9)0.5+1 # y = f(X) = (0.5 + 1) (5) + c =f(x) = 2 15(5X + 9)3/2 + c1) This question's solution is 100% correct width = ( ) - 148 14 ( 2 cos # 2 ) 12 12 4- 8. 81 type only two digit after decimal 2 ; ) This question is also correct The value of a is calculated by putting equation - to o 1.e., 2 za sinh ( 35 ) = 71 I for value of a = 119-5 LM'S = RHS :. a = 119 - 5 and at last , we calculated from equation y ( 35) = (16- 119.5)+ 119. 5x cosh ( 35 = 21 . 16 ft Jupto 2 decimal place